From my experience, you would first want to harden it, then temper it.
When you harden it, some steels are quenched with water and some with oil. Always start with the oil, it does not quench as fast, if you start with water and it quenches to fast, the steel will develop hairline cracks and will cause failure.
Here is some good info from Metalsmith V21.2
Hardening and Tempering
Hardening
If steel is heated to a high temperature, bright or cherry red, and then quenched in oil or water, the atoms of iron and carbon re-arrange themselves in a formation which give the metal a very hard and brittle property. This process is known as hardening. If this metal is heated again to a lower temperature, dull red, and allowed to cool slowly it will revert to its soft state. Hardened steel if only partially re-heated will lose its brittleness and springiness will appear as the heat increases. This process is known as tempering. A pretty simple explanation of heat treating but all you need to know to turn pieces of stock into a serviceable spring. Selecting the right heats will require some experimentation. Every metal treating, blacksmithing, gunsmithing book and even in what I have written here speaks of heats in colors. Ever notice how many colors mother nature uses in painting cherries, and we all speak of cherry red. Cherry red, in medium sunlight, is approximately 1500 degrees. On an overcast day, in a dim shop, 1500 degrees will appear brighter and in bright sunlight will seem duller. A hint: What we are looking for is the 'critical heat", when you reach this heat the magnetic attraction of the metal will disappear. When all else fails the use of one of the temperature testing products such as Tempilaq or Tempilstick comes in handy especially for some of us that are color blind to most shades of red. When your stock reaches this heat quench it in OIL, moving it around so that it cools evenly. Your spring is now very hard and brittle.
Tempering
The next step is to reduce this hardness by tempering. The ideal temperature for tempering steel with .6 to .7 % carbon is 700 degrees f. This may be accomplished in several ways.
a.) Lead melts at about this temperature and you may submerge the spring in molten lead until it reaches the point that the lead no longer sticks to it. Submerge the part fully, and remember that steel floats in lead.
b.) Self-cleaning ovens 700 degrees in their cleaning cycle and you can clean your electric oven and temper the spring at the same time, (My wife hates this trick).
c.) Fiercely burning motor oil burns at about this temperature. if you fill a shallow tin with oil to cover the spring and heat it with a torch until it sputters and burns with a roaring flame until the oil burns away you will reach 'draw' or temper.[TABLE="width: 80%"]
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[TD]You may have read that springs should be tempered until they are blue. If you polish a piece of steel and heat it slowly until various colors appear. The blues begin to appear at about 580 degrees, at this temper you are in danger of having your spring still brittle and it may break.[/TD]
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After the above has been done the spring is ready for final polish. before any polish is done examine the spring with a magnifying glass to detect any flaws.
Cracks of a circular form in the corners indicate uneven heating. Start again!
Cracks of a vertical nature or dark fissures indicate the steel has been burned. Start again!
Dimples, show that there are hard and soft places and indicate that the heating and cooling has been uneven. Start again!
When the spring is perfect in ever respect polish it to mirror finish and place it under test**.
